Received February 01, 2011, in final form June 02, 2011; Published online June 15, 2011

Abstract
A signature independent formalism is created and utilized to determine the general
second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds.
The formalism is used to characterize the orthonormal frames and metrics that permit
the solution of Dirac's equation by separation of variables in the case where a second-order
symmetry operator underlies the separation. Separation of variables in complex variables on
two-dimensional Minkowski space is also considered.

Chandrasekhar S.,
The mathematical theory of black holes, International Series of Monographs on Physics, Vol. 69, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1983.